The Hadronic Horizon: Deriving Quantum Chromodynamic Confinement and the 10⁻¹⁵ m Scale from the Ramanujan-Hernández Modular Framework

Color confinement and the origin of the hadronic scale (μ ≈ 10-15 m) remain outstanding challenges in Quantum Chromodynamics (QCD) due to the inherent infrared divergences of the continuous C∞ spacetime manifold. In this work, we demonstrate that the strong nuclear force emerges naturally as an elastic response and a hyperviscous breakdown of a discretely structured spacetime fabric. By introducing a non-linear continuous latency function ΓHV(r) coupled to the Hérnández-Valdivia Limit (εHV), we model the dynamic transition between asymptotic freedom at short distances and topological rigidity at the femtometric scale. Under this framework, the gluon flux tube acts as a high-density information channel that saturates the localized state density of the vacuum's simplicial complex. Upon reaching the critical threshold of 10-15 m, the geometric resistance becomes asymptotically infinite, enforcing absolute confinement without requiring ad-hoc scalar fields. Finally, by integrating the Callan-Symanzik equations under the action of the quadratic Ramanujan-Hérnández modular packing density (ΦRH2), we mathematically derive the hadronic horizon as a strict consequence of an ultraviolet topological fixed point, thereby unifying high-energy gauge dynamics with discrete spacetime geometry.